2018/08/09 by Matthew Corsetti, Ernest Fokoué · 1 citation
Computer Science · Mathematics · #Advanced Image and Video Retrieval Techniques #Algorithm #Artificial intelligence #Basis (linear algebra) #Combinatorics #Computer science #Face and Expression Recognition #Factorization #Function (biology) #Image Retrieval and Classification Techniques #Low-rank approximation #Mathematics #Matrix (chemical analysis) #Matrix decomposition #Multiplicative function #Non-negative matrix factorization #Nonnegative matrix #Pattern recognition (psychology) #Pure mathematics #Rank (graph theory) #Symmetric matrix #Toeplitz matrix #cs.LG #msc:62H35 #stat.ML
paper · pdf · doi:10.26713/jims.v10i1-2.851
published in Journal of Informatics and Mathematical Sciences 10(1-2), 201-215 · 15 pages, 6 figures, 3 tables
openalex publication_date 2018/08/09 · arxiv created 2020/12/07 · arxiv updated 2020/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Nonnegative Matrix Factorization (NMF) is an unsupervised learning algorithm that produces a linear, parts-based approximation of a data matrix. NMF constructs a nonnegative low rank basis matrix and a nonnegative low rank matrix of weights which, when multiplied together, approximate the data matrix of interest using some cost function. The NMF algorithm can be modified to include auxiliary constraints which impose task-specific penalties or restrictions on the cost function of the matrix factorization. In this paper we propose a new NMF algorithm that makes use of non-datadependent auxiliary constraints which incorporate a Toeplitz matrix into the multiplicative updating of the basis and weight matrices. We compare the facial recognition performance of our new Toeplitz Nonnegative Matrix Factorization (TNMF) algorithm to the performance of the Zellner Nonnegative Matrix Factorization (ZNMF) algorithm which makes use of data-dependent auxiliary constraints. We also compare the facial recognition performance of the two aforementioned algorithms with the performance of several preexisting constrained NMF algorithms that have non-data-dependent penalties. The facial recognition performances are evaluated using the Cambridge ORL Database of Faces and the Yale Database of Faces.